The Area Of A Circle Calculator
Circle area is pi times the radius squared. Everything difficult about the topic sits in two decisions: which length is the radius, and how much precision you carry.
Area of the circle
153.938
- Circumference
- 43.9823
- Diameter
- 14
- Area of the sector at that angle
- 38.4845
- Arc length at that angle
- 10.9956
Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.
The formula this calculator uses
Area = pi x r^2
- r
- Radius — measured from the centre to the edge
- d
- Diameter — edge to edge through the centre, equal to 2r
- pi
- About 3.14159, the constant ratio of circumference to diameter
- C
- Circumference, equal to 2 x pi x r
How to check the result by hand
- 1
Establish whether you have a radius or a diameter
A radius runs centre to edge; a diameter runs edge to edge through the centre. Packaging almost always quotes diameter, so halve it before anything else.
- 2
Square the radius
7^2 = 49. This step is what makes the relationship quadratic, and it is why unit errors here are amplified rather than merely copied.
- 3
Multiply by pi, keeping plenty of digits
49 x 3.141592653589793 = 153.93804. Use pi at full precision in the calculation and round only the displayed result.
- 4
Compute circumference and diameter alongside
Circumference is 2 x pi x 7 = 43.98230 and diameter is simply 14. Having all three together lets you spot a scale error instantly.
- 5
Round once, at the end, to a defensible precision
If the radius was measured as 7 centimetres, quoting 154 square centimetres is honest while quoting 153.9380400259 is not.
For worked examples, common mistakes and the limits of this formula, read the full How To Calculate The Area Of A Circle page.